Multiple choice

From a pack of $52\ cards$, face cards and tens are removed and kept aside, then a card is drawn at random from the remaining cards. If A: The events that the card is drawn is an ace. H: The events that the card is drawn is a heart.S: the events that the card is drawn is a spade. Then, which of the following holds?

  1. $9P(A)=4P(H)$
  2. $P(S)=4P(A\cap H)$
  3. $3P(H)=P(A\cap S)$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
AI explanation

Removing the 12 face cards and the four tens leaves 36 cards, of which 4 are aces, so P(A) equals 4/36 or 1/9. The remaining 36 cards include 9 hearts, making P(H) equal to 9/36 or 1/4. Multiplying P(A) by 9 gives 1, and multiplying P(H) by 4 also gives 1, which verifies the equation 9P(A) = 4P(H).

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